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Speaker: Slawomir Solecki (Cornell)

Abstract:

The behavior of a measure preserving transformation, even a generic one, is highly non-uniform. In contrast to this observation, a different picture of a very uniform behavior of the closed group generated by a generic measure preserving transformation $T$ has emerged. This picture included substantial evidence that pointed to these groups (for a generic $T$) being all topologically isomorphic to a single group, namely, L0L^0L0—the topological group of all Lebesgue measurable functions from $[0,1]$ to the circle. In fact, Glasner and Weiss asked if this is the case.

We will describe the background touched on above (including all the relevant definitions) and outline a proof of the following theorem that answers the Glasner–Weiss question in the negative: for a generic measure preserving transformation $T$, the closed group generated by $T$ is not topologically isomorphic to L0 L^0 L0. The proof rests on an analysis of unitary representations of L0 L^0 L0.